This thesis encompasses theoretical and computational studies of strongly correlated electron systems. Understanding how electrons in solids interact with each other is of great importance for future technology and other applications.

This thesis encompasses theoretical and computational studies of strongly correlated electron systems. Understanding how electrons in solids interact with each other is of great importance for future technology and other applications. From a fundamental point of view, the Coulomb interaction in a solid leads to a very challenging many-body problem, encapsulating many physical phenomena, e.g. magnetism. Treating this interaction, with a focus on local contributions, is the subject of this thesis. Both models and materials have been investigated, to obtain insight on the mechanisms determining the macroscopic properties of matter. This thesis is divided in four parts, each corresponding to a different project or topic.

In the ﬁrst project a many body method called dynamical mean ﬁeld theory (DMFT) is used to study the paramagnetic phase of the Hubbard model. A stochastic version of the exact diagonalization technique is developed for solving the effective impurity model arising in DMFT and generating real frequency spectral functions. In the next project, by combining density functional theory (DFT) with a static solution of the DMFT equations (DFT+U), magnetic exchange interactions in transition metal oxides (TMOs) are investigated. The spin dependence of the functional is shown to be important for mapping magnetic excitations form the quantum mechanical system to a classical model.

The next topic in this thesis concerns the x-ray absorption spectroscopy of TMOs. Spectral functions, in good agreement with experimental data, are calculated by combining DFT with multiplet ligand ﬁeld theory (MLFT). The effects of the presence of a core-hole are studied in detail for NiO, as well as double counting issues related to higher order terms of the multiple expansion of the Coulomb interaction. A strained induced linearly polarized spectrum is obtained for CaTiO3. Lastly, charge disproportionation is seen in Mo doped LaFeO3.

Finally, a critical step in DMFT, called analytical continuation, to obtain physical observables of interest is investigated. Analytical continuation means a transformation of a function in the complex plane. Several methods for performing this transformation are explained, and in particular steps for improving the robustness and accuracy of the Padé approximant method are described.